Relations between the maximum modulus and maximum term of entire functions (Q1064430)

Relations between the maximum modulus M(R) and the maximum term \(\mu\) (r) of an entire function are investigated by the author. The author derives several such relations. One which gives a clear upper bound for M(r) is the following: Theorem. For every \(R>\epsilon >0\) we have \[ M(R)<((4R+\epsilon)/\epsilon)(1+\log (\mu (R+\epsilon)/\mu (R))^{\mu (R)}. \] This paper is written in memory of Ernst Straus.